Mathematics for FinanceMTP Sep 24 Series IQuestion 1425 of 512
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If the interest rate on a loan at 1%\displaystyle 1\% per month, the effective annual rate of interest is:

Options

A12%\displaystyle 12\%
B12.36%\displaystyle 12.36\%
C12.68%\displaystyle 12.68\%
D12.84%\displaystyle 12.84\%
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Correct Answer

✅ Option c — 12.68%\displaystyle 12.68\%

All Options:

  • A12%\displaystyle 12\%
  • B12.36%\displaystyle 12.36\%
  • C12.68%\displaystyle 12.68\%
  • D12.84%\displaystyle 12.84\%

Detailed Solution & Explanation

Given parameters: * Monthly Interest Rate (i\displaystyle i) = 1%\displaystyle 1\% per month =0.01\displaystyle = 0.01 * Number of compounding periods per year (m\displaystyle m) = 12\displaystyle 12 The formula for the effective annual rate of interest (E\displaystyle E) is: E=(1+i)m−1E = (1 + i)^m - 1 Substituting the values: E=(1+0.01)12−1E = (1 + 0.01)^{12} - 1 E=(1.01)12−1E = (1.01)^{12} - 1 First, let's calculate (1.01)12\displaystyle (1.01)^{12}: (1.01)12≈1.126825(1.01)^{12} \approx 1.126825 Thus: E≈1.126825−1=0.126825=12.68%E \approx 1.126825 - 1 = 0.126825 = 12.68\% The effective annual rate of interest is 12.68%\displaystyle 12.68\%. Hence, **Option C** is the correct answer.

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